8y+84=3y2-y

Solution for 8y+84=3y2-y equation:

8y+84=3y^2-y

We move all terms to the left:

8y+84-(3y^2-y)=0

We get rid of parentheses

-3y^2+8y+y+84=0

We add all the numbers together, and all the variables

-3y^2+9y+84=0

a = -3; b = 9; c = +84;
Δ = b2-4ac
Δ = 92-4·(-3)·84
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-33}{2*-3}=\frac{-42}{-6}
=+7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+33}{2*-3}=\frac{24}{-6}
=-4
$